Many real-world signal processing problems involve elements of non-Gaussianity, non-linearity and non-stationarity. Consequently, it is not usually possible to derive exact closed form estimators based upon the standard criteria of maximum likelihood, maximum a posteriori or minimum mean-squared error. Classical sub-optimal methods, such as extended Kalman filters and Gaussian sum approximations are easy to implement. However, they do not take into account all the salient statistical features of the processes under consideration, thereby often leading to poor results.

The advent of cheap and massive computational power, in conjunction with some recent developments in applied statistics, have stimulated many advancements in the field of Sequential Monte Carlo simulation. Monte Carlo methods are very flexible in that they do not require any assumptions about the probability distributions of the data. Moreover, experimental evidence suggests that these methods lead to improved results. From a Bayesian perspective, Sequential Monte Carlo methods allow one to compute the posterior probability distributions of interest on-line. Yet, the methods can also be applied within a maximum likelihood context. As a result, they are being applied to a large number of interesting real problems such as computer vision, econometrics, medical prognosis, tracking, communications, blind deconvolution, statistical model diagnostic tools, automatic control, navigation and neural network training among others.